Can we say "the set of all functions between two sets" as easily as we could say "the set of all real numbers", for example?

  • $\begingroup$ Do you mean between two specific sets, or the class of all functions? $\endgroup$ – copper.hat Mar 13 '14 at 6:15
  • $\begingroup$ I mean GIVEN two sets. $\endgroup$ – PatrickMcGill Mar 13 '14 at 6:29

Yes. This is allowed because, set theoretically, functions $A \rightarrow B$ are special subsets of $A \times B$. Sets are closed under cartesian products and comprehension allows you to take arbitrary subsets (as long as you're able to specify the membership condition in your logic).


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